Hello I am working on an accounting problem using reciprocal method of allocation which is basically a matrix algebra. However, I cannot seem to solve the following.

Please advise. I need to find what X, Y, and Z equal to.

X Y Z

X .2 .1 .2

Y .4 .1

Z .0909

COST

X 100,000

Y 50,000

Z 40,000

So I am assuming the first function is: X=100,000 + .2X + .4Y

I am not sure if this is correct. Should it be X=100,000 + .4Y

Please advise as to how to solve this problem.

Thank you for any help or guidance.